On 𝐹𝐾-spaces which are boundedness domains

Meyers, Glenn

doi:10.1090/S0002-9939-1974-0372584-8

On $FK$-spaces which are boundedness domains
HTML articles powered by AMS MathViewer

by Glenn Meyers PDF

Proc. Amer. Math. Soc. 46 (1974), 38-42 Request permission

Abstract:

An open question in summability theory is to characterize those FK-spaces, $E$, which are boundedness domains (i.e., $E = {m_A}$ for some infinite matrix $A$). As a partial solution to this problem we give necessary and sufficient conditions for an FK space $E$, which has the $T$-sectional boundedness property, to be equal to ${m_A}$ for some row-finite $A$.

References

G. Bennett, A new class of sequence spaces with applications in summability theory, J. Reine Angew. Math. 266 (1974), 49–75. MR 344846, DOI 10.1515/crll.1974.266.49
Martin Buntinas, On Toeplitz sections in sequence spaces, Math. Proc. Cambridge Philos. Soc. 78 (1975), no. 3, 451–460. MR 410163, DOI 10.1017/S0305004100051926
Glenn Meyers, On Toeplitz sections in $FK$-spaces, Studia Math. 51 (1974), 23–33. MR 348445, DOI 10.4064/sm-51-1-23-33
Albert Wilansky, Functional analysis, Blaisdell Publishing Co. [Ginn and Co.], New York-Toronto-London, 1964. MR 0170186
Albert Wilansky and Karl Zeller, A biorthogonal system which is not a Toeplitz basis, Bull. Amer. Math. Soc. 69 (1963), 725–726. MR 151819, DOI 10.1090/S0002-9904-1963-11003-4